The late, great Australian art critic Robert Hughes once complained that “Crocodile Dundee” is still regarded by many Americans as a work of social realism. A rhetorical exaggeration, of course, but he had a point.

As an Australian living in the U.S., I’ve long been puzzled at the dominance of charming clichés about the country as a sun-dappled frontier. Advertising campaigns still promote the “ocker” image — Australian for redneck — depicting beer-swilling, happy-go-lucky folk barbecuing steak at the beach.

I protest to friends in vain that Australia has a lot more to offer than rampant hedonism and cuddly koalas. Its cities are wildly cosmopolitan, I argue, and even, dare I say, sophisticated. Its museums are packed, its cultural life raucous, and endless arts festivals clutter the social calendar.

The gulf between image and reality is most extreme in Sydney, my hometown, which is renowned for its Rio-like natural beauty. It’s also known for the Sydney Opera House, an instantly recognizable piece of architecture — although few Americans seem to consider that opera is actually performed there.

Heroically, on my most recent visit, I resisted the siren call of Sydney Harbor and the beaches. Instead, I stalked the creative populace, who exist in a parallel dimension to the classic tourist trail. Over the next 10 days, I was reminded just how original and imaginative Sydney’s inner life could be.

First stop, a check-in at the QT, a psychedelic “art hotel” that bills itself as an “urban playground.” It was a long way from the glitzy high-rise lodgings that are the vogue in Sydney. The new hotel is installed within a restored menswear store from the 1920s, and its décor evokes a Jean Cocteau dream sequence set in a high-class bordello.

The QT was the ideal base to explore the “inner city,” made up of bohemian neighborhoods surrounding the central business district that many first-time visitors often don’t even notice.

As a sentimental gesture, I hopped a cab straight to Edward Street, where I used to live as a student in a gritty neighborhood called Chippendale. The streets were now quiet and leafy, and my old flophouse-terrace was freshly painted and overflowing with flowers.

Even more shocking, Chippendale has been established as a nonprofit “Creative Precinct” with its own “Urban Walkabout” art tour. A foldout map directed me to galleries with names like Pompom and Kaleidoscope, as well as White Rabbit, a former factory that now houses a cutting-edge museum of Chinese contemporary art, complete with soothing teahouse.

Nearby, a Gothic Revival church had been turned into the NG Art Gallery, where a reception was in full swing.

However, the most evocative art site was tucked away in Surry Hills, back near the busy business center: the studio of Brett Whiteley, whose voluptuous use of light and color redefined modern Australian painting.

Strolling around the promenade of Circular Quay, another popular tourist spot, I averted my eyes from the green-and-yellow harbor ferries departing for white-sand beaches, to read the edifying plaques of the Sydney Writers Walk underfoot.

Each bronze disc offers quotes from local wordsmiths, some obscure to outsiders (colonial poet Henry Lawson), others recognized (Patrick White, Nobel Prize laureate of 1973), as well as a couple of American literary visitors, Jack London and Mark Twain.

I was starting to accept that every art experience in Sydney is somehow enhanced by nature. The stroll to the Art Gallery of New South Wales passed eucalyptus groves alive with native birds. “La Bohème” at the Opera House was preceded by cocktails on a balcony in the velvety summer dusk.

A play at the Sydney Theater Company was followed by an oyster supper at the End of the Wharf, where you can casually watch watercraft parading below.

“I think the physical beauty of Sydney is an important element for a sense of possibility in the arts,” director Neil Armfield, who worked with such young unknowns as Cate Blanchett, Hugo Weaving and Geoffrey Rush, told me later.

“When you grow up here, you have a sense of being surrounded by something miraculous. It alters the framework inside of you somehow.”